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Which expression is equivalent to $(4^2)^8$ ? $\newline$ Choices: $\newline$ (A) $4^{16}$ $\newline$ (B) $\frac{1}{4^{16}}$ $\newline$ (C) $4^{10}$ $\newline$ (D) $\frac{1}{4^{10}}$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

(4^2)^8

?

\newline

Choices:

\newline

(A)

4^{16}

\newline

(B)

\frac{1}{4^{16}}

\newline

(C)

4^{10}

\newline

(D)

\frac{1}{4^{10}}

Understand and Apply Power Rule: Understand the problem and apply the power of a power rule. $\newline$ The problem asks us to simplify the expression \(4^ $2$ )^ $8$ \. According to the power of a power rule, when we raise a power to another power, we multiply the exponents.
Apply Power of Power Rule: Apply the power of a power rule to the given expression. $\newline$ $(4^2)^8 = 4^{(2*8)} = 4^{16}$
Match Simplified Expression: Match the simplified expression to the given choices. $\newline$ The simplified expression is $4^{16}$ , which matches choice (A).
Confirm Accuracy: Confirm that no mathematical errors have been made. We have correctly applied the power of a power rule and have not made any calculation errors.

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